1. Technical Field
The present invention relates to an intermediate image generation method, apparatus, and program for generating an intermediate image which is an image in the middle of changing from one to the other of two pseudo three-dimensional images generated by ray casting a three-dimensional image under two different opacity level setting conditions.
2. Description of the Related Art
In order to facilitate understanding of a three-dimensional structure of a subject, image processing for generating and displaying a pseudo three-dimensional image which is three-dimensional image data of a subject, constituted by multiple two dimensional images obtained by a CT system, an MRI system, an ultrasonic diagnostic system, or the like, is stereoscopically visualized on a two-dimensional plane using computer graphics technologies.
As for the method of generating such pseudo three-dimensional images, a volume rendering method is known. This is a method for generating a translucent projection image by sampling, based on an opacity level and a luminance value set to each pixel (voxel) constituting a three-dimensional image, these values at each search point along each visual line and adding up the products of these values to obtain a pixel value of each pixel to be projected.
More specifically, as illustrated in FIG. 1, a plurality of search points Pji is set by sampling a three-dimensional image V at a predetermined interval along a plurality of visual lines Ej (j=1, 2, - - - , L; L represents the number of visual lines). Then, a luminance value b(Pji) and an opacity level f(Pji) of each search point Pji are obtained in series along the visual line Ej, and an output pixel value of a pixel, projected on a projection plane, through which the visual line Ej passes is determined by Formula (3) below. Such processing is performed on each visual line to determine the output pixel values of all projection pixels on the projection plane, whereby a projection image is generated.
                              C          j                =                              ∑                          i              =              1                        n                    ⁢                                          ⁢                      (                                          b                ⁡                                  (                                      P                    ji                                    )                                            ×                              f                ⁡                                  (                                      P                    ji                                    )                                            ⁢                                                ∏                                      k                    =                    1                                                        i                    -                    1                                                  ⁢                                                                  ⁢                                  (                                      1                    -                                          f                      ⁡                                              (                                                  P                          jk                                                )                                                                              )                                                      )                                              (        3        )            
Here, the opacity level f(Pji) of each search point Pji is determined according to the pixel value of the search point based on an opacity level predefined with respect to each pixel value. Therefore, by adjusting the setting of the opacity level allocated according to the pixel value, the visualization degree of the subject may be adjusted.
For example, as shown in FIGS. 2A to 4A, it is practiced to display, on a display screen, an image that changes from one side 1A to the other side 1B of two pseudo three-dimensional images generated under two different opacity level setting functions by providing sliding box 91 on the upper side of the display screen for displaying a projection image and sliding the position of slider 92 of slide box 91 from the left end (α=0) to the right end (α=1).
More specifically, when slider 92 is positioned at the left end (α=0), a setting function FA(g) shown in the graph of FIG. 2B is applied and, as shown in FIG. 2A, an image IA with completely transparent ribs is generated, while when it is positioned at the right end (α=1), a setting function FB(g) shown in the graph of FIG. 4B is applied and, as shown in FIG. 4A, an image IA with completely opaque ribs is generated. When slider 92 is positioned between the two ends (0<α<1), a setting function FH, obtained through linear interpolation of setting functions FA(g) and FB(g) by Formula (4) below according to the position α of slider 92, is applied and, as shown in FIG. 3A, an intermediate image IH in the middle of changing from image IA to image IB is generated as described, for example, in Japanese Unexamined Patent Publication No. 2005-202791.FH(g)=(1.0−α)FA(g)+αFB(g)  (4)
Note that the intermediate image shown in FIG. 3A is an image generated by applying the opacity level setting function FH (g) shown in the graph of FIG. 3B when slider 92 is positioned at α=0.2. Here, each of the projection images IA, IH, IB is an image, by way of example, formed of a projection image of ribs superimposed with a projection image of a heart generated by ray casting a three-dimensional image of the heart under a setting function FK (g) of a given opacity level.
In the conventional technology described above, the opacity level allocated to each search point changes linearly according to Formula (4) above with respect to a linear change in the position α of slider 92, but when Formula (3) is substituted by the setting function FH (g) of Formula (4) above, Formula (3) becomes an (n+1)-th degree polynomial function and changes in the output pixel values of projection pixels are mostly nonlinear.
For example, when generating a projection image that changes from a pseudo three-dimensional image IA generated under the condition of setting function FA(g)=0.0 to a pseudo three-dimensional image IB generated under the condition of setting function FB(g)=1.0 by volume rendering with the number of search points n=4 along the visual line Ei, the output pixel value C with respect to the changing phase α becomes like that shown in graph 71a of FIG. 5. In graph 71a, the output pixel value C changes sharply from the start of the change in α(α=0), and when the changing phase α is 0.2, the output pixel value C has already passed more than half of the entire change and the change in the output pixel value C becomes extremely small as the changing phase approaches its end (α=1).
Further, when generating a projection image that changes from a pseudo three-dimensional image IA generated under the condition of setting function FA(g)=1.0 to a pseudo three-dimensional image IB generated under the condition of setting function FB(g)=0.0, the output pixel value C with respect to the changing phase α becomes like that shown in graph 71b of FIG. 6.
In this way, the conventional technology described above has a problem that it can not obtain an intermediate image which changes linearly from one to the other of projection images only by linearly changing the changing phase α.
In view of the circumstances described above, it is an object of the present invention to provide an intermediate image generation method, apparatus, and program capable of, when generating an intermediate image which is an image in the middle of changing from one to the other of two pseudo three-dimensional images generated by ray casting a three-dimensional image under two different setting conditions for an opacity level to be allocated according to a pixel value, generating an intermediate image that appears to change substantially linearly with a linear change in the changing phase.